A population of values has a normal distribution with \( \mu=65.3 \) and \( \sigma=70.3 \). A random sample of size \( n=134 \) is drawn. a. What is the mean of the distribution of sample means? \( \mu_{\bar{x}}= \) b. What is the standard deviation of the distribution of sample means? Round your answer to two decimal places. \( \sigma_{\bar{x}}=\square \)

The mean of the distribution of sample means, often referred to as the expected value of the sample mean, is the same as the population mean. So, in this case, \( \mu_{\bar{x}} = \mu = 65.3 \). To find the standard deviation of the distribution of sample means, also known as the standard error, you use the formula \( \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} \). Plugging in the population standard deviation \( \sigma = 70.3 \) and the sample size \( n = 134 \), we calculate: \[ \sigma_{\bar{x}} = \frac{70.3}{\sqrt{134}} \approx 6.08. \] So rounding to two decimal places, \( \sigma_{\bar{x}} \approx 6.08 \).